An approach for the advanced planning of a reliability demonstration test based on a Bayes procedure

The classical theory to determine sampling plans yields a large sample-size which is necessary to demonstrate the product reliability. Above all, the sample-size increases tremendously, if failures have to be taken into account. To use all information about the product given through the development process the application of Bayes procedure is recommended. In the paper, it was suggested how to generate a prior distribution from fatigue damage calculations, preceding tests or the analysis of warranty data of a former product. We considered a case where the information about the reliability may not be given for the desired product lifetime but for any other time. Additionally, it was taken into account that prior information may be available from an accelerated test. When prior information is used there is always the uncertainty as to what extent the information about the reliability is valid for the actual product conditions. It is obvious that the information of a former product or preceding tests may not be totally transferable to the actual product concerning reliability. In this paper the so-called "decrease-factor" δ was introduced which artificially reduces the quality level of prior reliability information. A procedure for the estimation of the decrease-factor was suggested for a case where information about the failure behavior of a former product is utilized. In this context, the FMECA offers a useful foundation. In a synthetic example the reliability demonstration test was planned by using calculation results, results of a preceding test and the knowledge about the failure behavior of a former product. It was shown that the sample-size necessary to demonstrate the requirements increases with lower decrease-factors. Compared with the classical method it was possible to reduce the sample-size if prior knowledge is considered. The sample-size is reduced by 4 test items at least. For the best case where the prior information was totally used no subsequent test would be necessary. However, due to differences in test conditions or environment and function the total use of prior information is not recommended. To minimize the risk of failing to meet the product requirements the decrease-factor should be estimated with lower values than 1.